This invention relates to a method for removing coherent noise from seismic data. More specifically, this invention relates to an improved method for removing coherent noise from a series of seismic traces which correspond to a small group of geophones by exploiting the structure of an FFT/ME/EP (Fast Fourier Transform/Maximum Entropy/Extended Prony) model of the seismic data.
In seismic exploration, it is common practice to deploy a large array of geophones on the surface of the earth and to record the vibrations of the earth at each geophone location to obtain a collection of seismic traces. The traces are sampled and recorded for further processing. When the vibrations so recorded are caused by a seismic source activated at a known time and location, the recorded data can be processed by computer in known ways to produce an image of the subsurface. The image thus produced is commonly interpreted by geophysicists to detect the possible presence of valuable hydrocarbons.
Seismograms are commonly recorded as digital samples representing the amplitude of received seismic signal as a function of time. Since seismograms are usually obtained along a line of exploration on the surface of the earth, the digital samples can be formed into x-t arrays with each sample in the array representing the amplitude of the seismic signal as a function of horizontal distance and time. When such arrays are visually reproduced, by plotting or the like, seismic sections are produced. A seismic section depicts the subsurface layering of a section of the earth. It is the principal tool which the geophysicist studies to determine the nature of the earth's subsurface formation. Before an array of seismic samples or traces can be converted into a seismic section for interpretation by geophysicists, however, the array must be extensively processed to remove noise and to make reflection events discernable.
In the processing of seismograms, x-t arrays are sometimes transformed into arrays of complex numbers as a function of frequency and wavenumber. This is commonly referred to as a "frequency-wavenumber" or "f-k" transformation. The f-k transformation has been used as a tool to study and filter seismic data. F-k transforms are routinely used to represent data collected by large arrays of sensors, including seismic data. Usually, the f-k representations are computed by Fast Fourier Transforms (hereafter referred to as FFTs). The resulting data representations are parameterized by frequencies, wavenumbers (spatial frequencies), amplitudes and phases. In particular, for each frequency there is a collection of wavenumbers, and for each frequency-wavenumber pair there is a complex number representative of an amplitude and a phase. Among various applications of this representation are spectrum analysis (displaying of the amplitude squared as a function of frequency and wavenumber) and filtering in the frequency-wavenumber domain.
In U.S. Pat. No. 4,218,765 issued to Kinkade, seismic traces are transformed to an f-k array and filtering is performed on the traces in f-k domain. In U.S. Pat. No. 4,308,059 issued to Ruehle, multiple reflections are filtered from seismograms by transforming them into an f-k array representing amplitude as a function of frequency and wavenumber. In Ruehle, the f-k array of the seismograms is filtered by weighting all samples with the inverse of the f-k transform of the multiple reflections. In U.S. Pat. No. 4,594,693 issued to Pann et al., seismic trace interpolation is carried out by inserting zero amplitude traces between the seismic traces in a section where spatial aliasing is a problem. The traces are then transformed into an f-k array. The f-k array is filtered to reject samples in a region of frequency and wavenumber which exhibits aliasing. The filtered f-k array is then transformed back into a seismic section representing amplitude as a function of time and distance.
It is well known that seismic data can change appreciably in frequency and wavenumber from one place on the surface to another. Indeed, significant differences in the character of seismic energy has been found to occur within the distance spanned by feasible arrays of seismic geophones. It would be desirable, therefore, to process recorded seismic data as if it were sensed by a collection of subsets of geophones on the surface. For example, the first few traces describe the seismic data, and hence the subsurface, near one end of the spread of seismic geophones, while a few consecutive traces centered elsewhere within the spread of seismic geophones would describe the seismic data, and hence the subsurface, elsewhere. Significant differences between data at different locations can best be detected by separate processing of such small sets of consecutive traces. In particular, it would be desirable to analyze the data from each subset of sensors in terms of the frequency-wavenumber representations of the subsets of data. The collection of f-k representations of the data would provide a description of the spatial variation of the seismic data useful in analysis, filtering, and other applications.
While it would be desirable to process the recorded seismic data as if it were sensed by a collection of subsets of geophones on the surface, when a small number of seismic traces are used, such as when processing data from a subset of geophones, numerous undesirable side effects occur. For example, when using the FFT to obtain both frequency and wavenumber representations of the subset of seismic data, the FFT is corrupted by processing noise generally known as "sidelobes" or "Gibbs phenomenon". This processing noise results from transforming too few spatial data points and will degrade the traditional uses of f-k representations such as spectrum analysis and filtering. Traditionally, seismic exploration provides ample time samples so that corruption of the FFT by such side effects does not occur. It is only when processing seismic data where a limited number of spatial samples are available, such as attempting to process seismic data from a small subset of geophones, does such side effects prevent the f-k representation produced by FFT methods from being useful in analyzing the acquired seismic data.